Reefs and sand dunes are critical morphological features providing
natural coastal protection. Reefs dissipate around 90 % of
the incident wave energy through wave breaking, whereas sand dunes
provide the final natural barrier against coastal flooding. The storm
impact on coastal areas with these features depends on the relative
elevation of the extreme water levels with respect to the sand dune
morphology. However, despite the importance of barrier reefs and dunes
in coastal protection, poor management practices have degraded these
ecosystems, increasing their vulnerability to coastal flooding. The
present study aims to theoretically investigate the role of the
reef–dune system in coastal protection under current climatic
conditions at Puerto Morelos, located in the Mexican Caribbean Sea,
using a widely validated nonlinear non-hydrostatic numerical model
(SWASH). Wave hindcast information, tidal level, and a measured beach
profile of the reef–dune system in Puerto Morelos are employed to
estimate extreme runup and the storm impact scale for current and
theoretical scenarios. The numerical results show the importance of
including the storm surge when predicting extreme water levels and
also show that ecosystem degradation has important implications for
coastal protection against storms with return periods of less than
10 years. The latter highlights the importance of conservation of the
system as a mitigation measure to decrease coastal vulnerability and
infrastructure losses in coastal areas in the short to medium
term. Furthermore, the results are used to evaluate the applicability
of runup parameterisations for beaches to reef environments. Numerical
analysis of runup dynamics suggests that runup parameterisations for
reef environments can be improved by including the fore reef
slope. Therefore, future research to develop runup parameterisations
incorporating reef geometry features (e.g. reef crest elevation, reef
lagoon width, fore reef slope) is warranted.
Introduction
Coral reefs protect coastal regions against the natural hazards
associated with storm wave events, thereby protecting beaches against
processes of erosion. Energy dissipation at the coast is increased by
the presence of irregular reef surfaces, which are important in wave
transformation . These natural barriers can dissipate
up to 97 % of the incoming wave energy, with the reef crest
alone reducing wave height between 64 and 76 %. This property becomes
particularly important considering that approximately 850 million
people (one-eighth of the world's population) reside within
100 km of a coral reef, with more than 275 million living less
than 30 km from reefs, benefiting from the services they
provide . While coral reefs protect the coasts from
wave energy, wave-driven flooding along the coast can still occur
under extreme events such as hurricanes.
Coral reefs have been degrading over the last four decades
, as a result of a combination of factors including
overfishing, coastal development, contamination and an excess of
nutrients, as well as degradation by coral bleaching events due to
increased temperatures. reported erosion rates of
0.19 kgCaCO3 for a Panama reef, equivalent to
a vertical loss of approximately 6 mmyr-1. Considering that reef degradation reduces the
protective characteristics of coral reefs, there is an increase in
coastal vulnerability towards extreme events.
The degradation of coral reefs affects wave runup due to modifications
in the spatial gradient of wave dissipation, controlling both the
incident swash and wave-induced setup. Nevertheless, the impact of
a storm depends not only on the bathymetry and forcing parameters of
the storm but also on the geometry of the coast, particularly its
elevation . proposed
a scale that categorises storm-induced impacts and the magnitude of
net erosion and accretion on barrier islands based on the elevation of
extreme water levels relative to the elevation of geomorphic
features. Thus, sand dunes play an important role as natural barriers
against coastal flooding by attenuating wave energy and slowing inland
water transfer . After a storm, the height and
recovery of the dune are critical for determining the coast's
vulnerability to changes in sea level and storms
. Although a storm may cause a dune to erode, it
provides a source of sediment into the littoral cell
. This is not the case when the dune is removed by
increased coastal development and excessive exploitation of natural
resources, which puts these regions at greater risk from extreme
events.
According to a recent report on the importance of coral reefs and
dunes , the Caribbean is the region that
presents the greatest loss of dune vegetation, reducing dune stability
e.g. and hence its ability to provide natural
coastal protection. For the case of Cancún, Quintana Roo (Mexico),
since 1984 the beach has been receding by 2 myr-1 as
a result of the effects of hurricanes and coastal development
. Construction on the dunes of the barrier island has
restricted aeolic transport, thereby preventing the natural
regeneration of the dunes . On the other hand,
heights of 3–4 m have been observed for sand dunes in Puerto
Morelos .
pointed out that during the category 5 hurricane Wilma, in 2005, the
combined presence of dunes, a coral reef, and sand transported from
Cancún during the event protected the coast of Puerto Morelos. This
suggests that the coast is less vulnerable to extreme events where the
reef–dune system is conserved. Unfortunately, coastal dunes in Mexico
are at risk due to coastal or agricultural development
. Therefore, an assessment of the
implications of a reduction in natural coastal protection is required.
While there are a number of studies on the role of coral reef
e.g. and sand dune
e.g. geometry in coastal protection, fewer
look at their combined effect. Therefore, this study aims to
investigate the role of both reef and dune degradation on the storm
impact in Puerto Morelos (Mexico). The outline of the paper is as
follows. Section 2 describes the study area and the data employed in
this work. The numerical model is described in Sect. 3. Then, methods
used in this study are described in Sect. 4, followed by the results
(Sect. 5). A discussion on the applicability of current runup
parameterisations to this environment is presented in
Sect. 6. Finally, concluding remarks are provided in Sect. 7.
Site and data description
The Puerto Morelos fringing reef lagoon is located in the western
Caribbean, approximately 25 km south of Cancún, on the
northeast coast of the Yucatán Peninsula, Mexico
(Fig. a). This area is of particular
interest for several reasons, notably its economic importance for
tourism and fisheries (10 fishing cooperatives operate in the area),
and its ecological significance, forming a natural protected area.
(a) Map of the study area. The solid black line indicates
the location of the bathymetric transect used in the numerical model.
(b) Bathymetry obtained from the transect indicated on the map
(bathymetry courtesy of CONABIO), including a beach profile surveyed in March
2014 (courtesy of CINVESTAV-Mérida).
Puerto Morelos is characterised by a semi-diurnal microtidal regime
with a tidal range of less than 0.4 m. There
is also evidence of a low-frequency, energetic oscillation (∼0.4m), associated with the Yucatán Current and atmospheric
pressure which has a period of ∼15 days
. The wave climate is dominated by wind waves from
the Caribbean (south-southeast, SSE) generated by the trade winds. The
waves have an average annual significant wave height, Hs, of
0.8 m and a dominant spectral peak period, Tp, between 6
and 8 s. In this region, waves
exceeding a height of 2 m are considered high-energy waves,
which often occur during the northerlies season, locally known as
“Nortes”, when anticyclonic cold fronts descend over the Gulf of
Mexico into the Caribbean Sea during the winter months
. Between June and
October, tropical cyclones can occasionally generate large waves (Hs≈6–12 m; Tm≈6–12 s)
. One example of such a storm was Hurricane
Wilma, which made landfall on 23 August 2005 with Hs>12m and a Tp of 10–12 s (measured at a depth of
20 m) .
The coastline in the study area is protected by a fringing reef which
forms a relatively shallow lagoon of 3–4 m depth and a width
that varies from 550 to 1500 m. The reef
has a well-developed back-reef and crest consisting of relatively
shallow, submerged coral banks, which play an important role in
dissipating wave energy through an active surf zone, thereby
protecting the coast. The gently sloping fore-reef descends to an
extensive sand platform at a depth of 20–25 m. The shelf edge
is located at a depth of 40–60 m, followed by a subsequent
drop-off at approximately 10 km from the coast to depths
exceeding 600 m.
The width of the beach is relatively stable, ranging between
85 and 90 m, with a dune of approximately 4 m in
elevation, which has been degraded in many areas as a result of
coastal development. The beach profile used in the present study for
Puerto Morelos was measured using a differential global positioning
system (DGPS) and was provided by CINVESTAV-Mérida. From the beach
profile to a depth of 20 m, the bathymetry obtained from
CONABIO (http://www.conabio.gob.mx/informacion/gis/, last access: 5 April 2017) was used
(Fig. b). Wave information is available for a site
located at a depth of approximately 20 m offshore of the study
site from a 30-year hindcast (1979–2008) for the Gulf of Mexico and
the western Caribbean Sea . These data were
estimated using the third-generation spectral wave model MIKE 21 SW
forced with wind data from the North American
Regional Reanalysis (NARR) . The numerical model
was validated/calibrated in deep waters with wave buoys and altimeter
information . The model
performance was found to be satisfactory for the Caribbean Sea with an
r2 of 0.87 . The mean observed height
(Hs) and peak period (Tp) were
1.22 m and 6.70 s, respectively, compared to the mean
reanalysis/hindcast values of 1.31 m and 7.27 s (RMS of 0.33 mHs and 1.59 s for
Tp with correlation coefficients of 0.90 and 0.51, bias
of 0.09 and 0.57, and scatter index of 0.27 and 0.24,
respectively). Thus, this information is employed as a forcing
boundary condition in the numerical model.
Numerical model
The Simulating WAves till Shore (SWASH) model, which is
a phase-resolving nonlinear non-hydrostatic model
(http://swash.sourceforge.net, last access: 20 January 2017) developed at Delft University
of Technology , is used in depth-averaged mode in
this study. This numerical model solves the nonlinear shallow water
equations, including the terms for non-hydrostatic pressure, which
make it suitable for simulating wave transformation as a result of
nonlinear wave–wave interactions in the surf and swash regions. The
model is also capable of simulating wave–current interaction, wave
breaking e.g., wave transformation
on reefs e.g., and wave runup e.g.. Therefore, this numerical model is
suitable for conducting a numerical study on wave transformation and
wave runup in the Puerto Morelos reef lagoon. For further model
details, including model equations see .
Consistent with prior studies, a wave-breaking parameter (α) of
0.6 was used for all simulations. A bottom friction coefficient (cf)
of 0.014 (Manning) was used, which is equal to that reported
previously for a study involving a fringing reef
and is also similar to that reported by for
a numerical study on a fringing reef (0.015). Although likely to be
lower than values obtained in field studies, and being a constant
value may result in under- or overestimation of roughness for the reef
or beach, respectively, in the absence of measured values for the study
site, this coefficient was used in the numerical simulations. Thus,
this study focuses on the degradation of the reef–dune
morphology. Reef roughness changes also play an important role in wave
transformation . However, the study
of these effects is beyond the scope of the present work.
Reconstructed time series, including the extreme water level,
Rhigh, for the current reef profile using the 30-year hindcast
wave conditions (wave height and period; Hs and
Tp) and sea level (astronomical tide without storm surge)
(Z). (a–c) Black lines indicate available hindcast data and red
stars indicate the selected cases used to represent the complete time series.
(d) Blue line represents time series reconstructed from the
simulated results. Red stars indicate the cases used for reconstruction.
Rhigh=R2%+Z.
Methods
The methodology used in this study is as follows. Firstly, a subset of
wave conditions at a water depth of 20 m was selected from the
3-hourly 30-year wave hindcast. Selected wave conditions were
propagated along non-degraded and degraded beach profiles, with the
corresponding tidal level, from a depth of 20 m to the shore
using the SWASH model. Subsequently, the extreme runup R2% and
setup <η> were calculated from the water elevation
time series, corresponding to each simulated case, and were further
employed to re-construct the 30-year extreme water level hindcast
using an interpolation technique. Finally, the storm impact was
obtained for different return periods and different scenarios of reef
and dune degradation by coupling the extreme water level and dune
morphology.
Measured beach profile (solid black line) and idealised profile with beach extended beyond the dune (dashed grey line). Dhigh represents the dune crest and Dlow the foot of the dune. The degraded profiles (0.3 and 1.1 m) are indicated by the dotted dark grey and dashed black lines, respectively.
Simulated cases
A total of 87 664 sea states (Hs, Tp and
θ), one every 3 h, comprise the available 30-year wave
hindcast . Due to the computational effort
involved in simulating the entire data set, a subset of 600 cases was
selected, following the method presented by and
applied in . This method employs the maximum
dissimilarity algorithm (MDA) to obtain a subset of wave conditions
representative of a variety of sea states (see references for further
details). In the present study, the multivariate data included peak
period (Tp), significant wave height (Hs),
and mean sea level (tide + storm surge) (Z). The wave parameters were
obtained from the wave hindcast and when storm surge is neglected the
Z time series corresponds to the astronomical tide prediction for
the same period and location
(http://predmar.cicese.mx/, last access: 8 August 2016). In
accordance with , the deep-water multivariate data
are defined as
Xi*=Hs,i,Tp,i,Zm,i;i=1,…,N,
where N refers to the total sea states obtained from the wave
hindcast. The vector components were normalised in order to assign
them even weightings for the similarity criterion defined by the
Euclidean distance, and hence the dimensionless vectors are defined as
e.g.Xi=Hi,Ti,Zi;i=1,…,N.
The MDA is used to select a subset of M vectors
(D1…DM) from the sample data. First, one
vector is transferred to the subset from the data sample. Subsequently
the dissimilarity between each of the remaining elements in the data
sample and those in the subset is calculated and the most dissimilar
element is transferred to the subset. This is repeated iteratively
until M elements have been selected. The dissimilarity between
vector i of the data sample and vectors j of the subset R is
determined by
dij=||Xi-Dj||;i=1,…,N-R;j=1,…,R.
Subsequently, the dissimilarity between vector i and the subset R,
is obtained using
di,subset=min||Xi-Dj||;i=1,…,N-R;j=1,…,R.
Once the N-R dissimilarities have been calculated, the next data to be
selected have the maximum di,subset. The Euclidean
distance was calculated
as
||Xi-Dj||=Hi-HjD2+Ti-TjD2+Zi-ZjD2
Finally, the subset was denormalised using
Dj*=Hs,jD,Ts,jD,Zs,jD;j=1,…,M.
The 600 selected sea states were found to adequately represent the
whole sample, and were well distributed throughout the time series of
sea level and wave parameters (Fig. a–c), consistent
with prior studies e.g.. In the
model runs the dune profile was extended beyond the crest, assuming
a continuation of the slope measured in the profile, to complete the
model domain and to enable the effect of reducing the dune crest
values to be inferred (Fig. ). The model was run with
the original profile, which included the back of the dune, and with
the extended dune to test whether this affected the wave statistics,
and no significant differences were found.
Extreme water level calculation
Waves were propagated from a depth of 20 m using SWASH
. The SWASH domain extends from a water depth of
20 m to the shoreline (a distance of 2 km) with
a uniform mesh size of 0.1 m. The numerical model was forced
using a JONSWAP spectrum at the offshore boundary derived from the
Hs and Tp corresponding to the 600
selected cases from the 30-year wave hindcast and the corresponding
sea level according to the astronomical tide. The initial time step
was 0.025 s and simulations were sampled for 2700 s,
after 500 s of spin-up time.
For each sea state propagated in SWASH, the height of the bottom
profile at the wet–dry interface was used to extract the water
elevation, η(t), relative to mean sea level
. To obtain a continuous time series, this
location was tracked as the first grid point where water depth was
less than 0.01 m. Extreme runup (R2%), corresponding
to the 2 % exceedance value in accordance with
, was calculated for each run (see
Fig. ). Furthermore, the maximum wave setup at the
shoreline, which is the super-elevation of the mean water level due to
waves , was computed as the mean of the wave
runup time series (<η>). Subsequently, the extreme water
levels Rhigh=R2%+Z and Rlow=<η>+Z were calculated for each case in accordance with
and . Rlow
represents the low extreme sea level resulting from the setup, tidal
level and storm surge contributions (where applicable), consistent
with .
(a) Example of a section of the water level elevation time series η(t) extracted from the wet–dry boundary of the SWASH simulations, showing sea level (astronomical tide without storm surge), Z, runup maxima, R, and setup at the shoreline <η>. (b) The 2 % exceedance value was extracted from the cumulative distribution function (cdf) of the R values and subtracting Z.
Return value of Rhigh for the current reef profile (triangles), the reef degraded by 0.3 m (crosses), and for the profile with the reef degraded by 1.1 m (open circles).
The 30-year-long time series was reconstructed based on the extreme
water levels from the 600 selected sea states. The time series of
extreme water levels were reconstructed using an interpolation method
based on a radial basis function (RBF). Previous studies have
identified this method as one of the most suitable for interpolating
multivariate scattered data and it has been used to
reconstruct time series of wave parameters in coastal waters
e.g.. The difference
in the present study is that wave direction is not included. The
interpolation function is
RBFXi=pXi+∑j=1MajΦ||Xi-Dj||,
where Xi={Hs,i,Tp,i,Zi}; i=1,…,N represents each of the sea
states in the 30-year time series; Dj={Hs,jD,Ts,jD,Zs,jD}; j=1,…,M represents each of the M=600 cases
selected; p(Xi)=b0+b1Hsi+b2Tpi+b3Zi; ∥.∥ indicates the Euclidean norm; and Φ is the
radial basis function see. The RBF interpolation
was carried out as described in using an
algorithm developed by . Therefore, the RBF was
used to reconstruct the Rhigh and Rlow 30-year
time series for all bathymetric profiles studied.
The 30-year reconstructed time series of Rhigh (see blue
line in Fig. d) and Rlow (not shown) were
used to assess beach vulnerability under current beach profile
conditions (Fig. ). The return period for both the
30-year Rhigh and Rlow time series was
calculated as the inverse of the probability of a given
Rhigh or Rlow value using the annual maxima
data from the re-constructed 30-year time series. Figure
shows the return value for Rhigh for the simulations
conducted with the current scenario and considering reef degradation
scenarios based on 50-year projections of reef erosion values (see
Sect. 4.3) reported in the literature (Fig. ).
The storm impact scale proposed by for barrier
islands was used to illustrate the implication of changes in either
reef or beach morphology (reef crest height and dune elevation) with
respect to storm-induced water levels. The scale includes four storm
impact regimes (Table ), which depend on the
storm-induced water levels and dune elevation, defined as
Rlow (the astronomical tide, wave setup, and storm surge,
where included), Rhigh (the sum of the astronomical tide,
R2%, and storm surge, where included), Dhigh (dune
crest height), and Dlow (dune toe height). These regimes
were calculated for three different reef crest conditions: (i) present
condition, (ii) degraded by 0.3 m, and (iii) degraded by
1.1 m (see Fig. ). These scenarios were selected
based on 50-year projections of reported reef erosion values. For
instance, the vertical loss of 6 mmyr-1 reported by
was used for scenario (ii), whereas the value of
22 mmyr-1 reported by was used for
scenario (iii).
The erosion values reported in prior studies are a result of el
Niño and bleaching events, which resulted in massive coral
mortality and the subsequent erosion of the remaining limestone
structure . In recent decades, mass coral
bleaching has increased in intensity and frequency
, preventing shallow corals from recovering
and leading to their gradual disintegration . This
is primarily associated with increased temperature, ocean
acidification and sea level rise . Hence,
a projection of the above values was used assuming that reefs will
continue to erode at similar rates.
ResultsPresent conditions
The Rhigh and Rlow values associated with
different (1-, 3-, 5-, 7.5-, 10-, 15-, and 30-year) return periods were
used together with the beach morphology (Dhigh and
Dlow) to estimate the storm impact regimes proposed by
for the present conditions
(Table ). Based on the return values of
Rhigh and Rlow, the storm impact regime
associated with a yearly return period was “swash”, where the maximum
runup is less than the height of the foot of the dune
(Rhigh<Dlow). For return periods of 3–5 years,
the storm impact regime was “collision”, where the maximum runup
collides with the foot of the dune but falls below the dune crest
(Dhigh>Rhigh>Dlow). For a return
period of 7.5 years, the storm impact increases to “overwash”, where
runup overtops the dune crest and the sand transported landward is
lost from the system and does not return to the beach after the storm
(Rhigh>Dhigh). For return periods of 10 years or
greater, the storm impact is “inundation” where the sea level is
sufficient that it completely submerges the dune.
Storm impact regime for the 1-, 3-, 5-, 7.5-, 10-, 15-, and 30-year return periods, considering a Dhigh and Dlow of 1.9 and 1.3 m, respectively, for different degrees of reef degradation (0.3 and 1.1 m).
Storm impact regime for the 1-, 3-, 5-, 7.5-, 10-, 15-, and 30-year return periods, considering a Dhigh and Dlow of 1.3 m, for different degrees of dune and reef degradation.
(a) Wave setup, <η>, (b) incident swash (Sinc), (c) infragravity swash (Sig), and (d) extreme runup (R2%) against incident wave conditions. Black dots represent the data for the conserved reef profile, green the values for the reef degraded by 0.3 m, and red those associated with the reef degraded by 1.1 m.
Return value of Rhigh for the model run with the storm surge (open circles) and without (crosses) for the time period of 1993–2008.
Role of reef degradation
To investigate the role of reef degradation in the reduction of
coastal protection the current situation was compared with the
scenarios of 0.3 and 1.1 m degradation of the reef crest (see
Sect. 4.3). It is important to note that in the present study, reef
roughness is constant in all three scenarios to focus only on the
effect of the vertical degradation of the reef, although in reality
this would likely be accompanied by a loss of roughness. Numerical
results show a slight increase in R2% when the reef is
degraded by 0.3 m, whereas there is a significant increase in
R2% when the reef is degraded by 1.1 m. The Rhigh
results and the storm impact regimes for the different scenarios
support these findings (see Fig. and
Table ).
The effect of reef degradation varies depending on the intensity of
the storm. For instance, for storms with return periods of
approximately 1–2 years, the increase in Rhigh when the
reef is degraded by 1.1 m is almost 2-fold, whereas the reef
degradation of 0.3 m has no visible effect on
Rhigh for such return periods
(Fig. ). However, for return periods of 2.5–7.5 years,
there is a notable increase in Rhigh for the 0.3 m
degraded reef (up to 30 %) compared to the conserved scenario
(current reef). This is particularly important since most people
living on the coast are more likely to experience these storms several
times in their lifetimes and relying on the protection provided by the
reef will not suffice under a degraded scenario. For storms with
a return period of >10 years the Rhigh values are
similar for degraded and non-degraded scenarios. The behaviour of
Rhigh for larger wave heights is related to the role
played by the reef in wave breaking. Under small wave heights, the
reef plays an important role in this process; however, as waves become
larger they break further offshore than the location of the reef
crest, and hence the reef no longer plays such an important role. This
seems to occur for return periods of approximately 10 years or
greater. Furthermore, the larger the waves, the more the water depth
will increase due to wave setup, making the differences in
Rhigh due to reef degradation less noticeable
In order to explain the observed differences in Rhigh at
larger wave heights, the runup was separated into the incident
(Sinc=fp⋅0.5<S<fp⋅2) and infragravity (Sig=fp⋅0.1<S<fp⋅0.5) swash frequencies (Fig. b and c) and
setup (Fig. a). Furthermore, setup, swash and runup data
were analysed in further detail. The change in the importance of the
reef crest in the wave-breaking process seems to take place for
H0L01/2>30m (Fig. ). Prior to this
point there is a clear dominance in Sig and R2%
for the 1.1 m degraded scenario. This is particularly notable
in Fig. d, as demonstrated by the consistently larger
values of R2% for 1.1 m degraded scenario and
H0L01/2<30m, after which there is greater overlap
in the values for all three scenarios. For intermediate and large wave
conditions, wave setup (Fig. a) seems to be slightly
greater for the non-degraded scenario as a result of the more intense
wave breaking occurring over the reef crest compared to the degraded
scenario. However, for the degraded scenario the infragravity
contribution is generally greater (Fig. c). The clear
increase in R2% for the degraded scenario demonstrated by
Fig. d reiterates the importance of the reef in
protecting the coast from flooding.
Regarding the storm impact regime (Table ), for a return
period of 5 years, there is an increase from a collision regime to an
overwash regime when the reef is degraded by 0.3 m. The
importance of the reef in protecting the coast becomes more obvious in
the scenario where the reef is degraded by 1.1 m, showing an
increase in the storm impact. Based on the results, the degraded
1.1 m scenario will result in the net erosion of the dune
(i.e. collision regime) even for a storm with a yearly return period,
whereas inundation will occur for a return period of 7.5 years.
Role of dune degradation
The dune crest elevation is a relevant parameter in coastal protection
against extreme water levels. Therefore, the implications of dune
degradation can be theoretically investigated by considering a smaller
crest elevation (Dhigh<1.9m) while estimating the
storm impact scale. Model results show that for return periods of
3–10 years the dune degradation by 0.6 m
(Table ) plays a more important role in coastal
protection than the reef crest when degraded 0.3 m
(Table ). Moreover, moderate reef degradation and dune
degradation together can be more important than the extreme reef
degradation of 1.1 m (see Table ). Therefore,
results show the combined importance of conserving the reef–dune
system in order to naturally protect the coast from storm
conditions. This is consistent with the results of
, who found that the greatest nature-based coastal
protection is offered when several habitats are considered.
Role of storm surge
To investigate the storm surge contribution, sea level data were
obtained from the HYbrid Coordinate Ocean Model
HYCOM; for the Gulf of Mexico
(GoM) (https://hycom.org/data/goml0pt04, last access: 12 October 2017) for the dates that
coincide with the available wave hindcast information
(1993–2008). For the GoM, HYCOM has a 1/25∘ or 0.04∘
equatorial and latitudinal resolution (∼3.5km) for each
variable at mid-latitudes. The version of HYCOM used is 2.2.77. Both
Hs and Tp from the Hindcast data were
interpolated to the same time vector as that of the GoM sea level
data. A total of 300 representative cases were simulated for the
16-year period (using the same methodology as for the 30-year
hindcast), using (i) the sea surface height obtained from HYCOM (mean
sea level including storm surge and astronomical tide) or (ii) the
astronomical tide. Figure shows Rhigh as
a function of the return period while considering the two different
scenarios. An increase in Rhigh is observed when storm
surge is included. This increase is important since it acts as a proxy
for reef degradation. Neglecting the storm surge contribution results
in an underestimate of the effects of reef degradation on runup and
hence coastal flooding. However, the effect of the storm surge (for
the time period available) was smaller than the effect of the reef
degrading by 1.1 m but slightly greater than the reef
degrading by 0.3 m, particularly for return periods of less
than 3 years (Fig. ).
(a) Significant wave height (Hs), (b) peak period (Tp), (c) sea level (Z) (black: astronomical tide; grey: GoM sea level) and (d)Rhigh (black: without the storm surge; grey: with storm surge) during the pass of Hurricane Wilma (2005).
(a) Incident swash, (b) infragravity swash and (c)
wave setup parameterised in a dimensional form of the Iribarren equation and
in comparison to Stockdon et al. (2006) (blue lines) and a modified form for
wave setup, which includes the reef face slope (red line). Black dots
represent the selected hindcast cases, green the values associated with high
water levels (Z≥Z15%=0.1636m), and red those associated with
low water levels (Z≤Z15%=-0.1636m).
Extreme runup values (R2%) for the selected 30-year hindcast data (black dots) and the complete parameterisation suggested by Stockdon et al. (2006) with the beach face slope (blue line) and reef face slope (red line).
In order to study the effects of the storm surge on extreme water
levels for the specific case of a hurricane event, wave parameters
were selected from the hindcast data between 19 and
25 October (Fig. a and b),
corresponding to Hurricane Wilma, a category 5 hurricane, which
reached the Yucatán Peninsula on 20–21 October 2005. The maximum Rhigh values are higher and
the minimum values are lower owing to the storm surge contribution
during the hurricane passage. In terms of reef degradation and the
effects of the storm surge during the hurricane, the Rhigh
values are generally greater for the degraded profiles throughout the
5 days presented, except around the peak of the hurricane (results
not shown). This might be ascribed to waves breaking further offshore
of the reef crest. Therefore, the storm impact during more extreme
conditions appears to be less sensitive to reef crest degradation than
during moderate storm conditions, further supporting the reef
degradation results presented in Sect. 5.2. It is also important to
note that during an extreme event, such as Hurricane Wilma, the reef
can act as a barrier against sediment transport, further reducing the
storm impact on the coast by retaining sand in the lagoon and on the
beach. However, this is not taken into account in the present study,
nor is the effect of changes in reef roughness associated with
degradation, which have been shown to have important implications in
wave transformation and wave runup
but are not the focus of the present
study. Furthermore, it is likely that by treating the dune as
a non-erodible feature, overtopping is underestimated.
Discussion
The calculation of extreme runup is necessary to estimate the storm
impact in coastal areas. Under certain combinations of energetic wave
conditions on fringing reefs, the steep reef face has been shown to
facilitate the liberation of fluctuations with infragravity periods,
which can pass into the lagoon with little energy loss and exacerbate
the effect of the storm . The importance of these
long-wave motions inside the lagoon has been previously demonstrated
by . The above phenomenon can be intensified if
the reef lagoon resonates with the wave period, amplifying the peak
energy of the surf beat . The
results of the current study show the dominance of infragravity swash
contributions. In order to look at this further, Sinc
vs. Sig variance was plotted against the Iribarren number
(not shown), showing a clear dominance of Sig
contributions under practically all wave conditions, reiterating the
importance of infragravity contributions in these environments.
With regards to the effect of habitat degradation, the results show an
increase in runup and hence storm impact with degradation,
particularly for storm periods of <10 years. Since the results show
that sand dunes also play an important role in coastal protection, in
locations where the presence of significant sand dunes along reef
fringed coastlines is rare e.g. Pacific
Islands;, an increase in runup as a result of reef
degradation will be even more detrimental. This becomes particularly
important as more people are exposed to sea level rise and coastal
hazards (e.g. erosion, flooding, and hurricanes) due to coastal
population growth .
Runup parameterisations provide a rapid assessment of coastal
vulnerability and hence deserve further investigation. Therefore,
runup dynamics and the validity of applying parameterisations used for
beaches in reef environments are investigated here. Incident and
infragravity swash height have been analysed for the conserved
scenario using the parameterisations proposed by ,
where the swash height was calculated as follows:
S=(Sinc)2+(Sig)2,
where Sinc and Sig are significant swash
height in the incident and infragravity frequencies, respectively. For
beaches, found incident swash height
(Sinc) to be best parameterised by a dimensional version
of an Iribarren-type relationship,
Sinc=0.75βH0L01/2, where β is the beach
face slope and H0 and L0 incident wave height and length,
respectively. Figure a shows the incident swash height
for the 600 cases simulated in the present study (high and low water
contributions are presented in green and red, respectively). As shown
in the figure, Stockdon's parameterisation (blue solid line) works
fairly well for Sinc, particularly for high water levels,
although it slightly overpredicts the numerical
results. Figure b shows the parameterisation for
infragravity swash height (Sig), excluding beach slope in
the parameterisation as suggested by , which also
works satisfactorily for the high-water level, although it is less
applicable for more energetic waves.
With regards to wave setup <η>, the parameterisations
presented by significantly underestimate wave
setup in the study area (Fig. c). The effects of the
relative contributions of high and low water to wave setup are less
obvious for this profile than for sandy beaches
e.g.. When the slope of the reef face is used
instead of the beach face slope, the parameterisation improves (red
vs. blue line Fig. c), although it still underestimates
the setup values.
Finally, when analysing R2% and comparing it to the complete
parameterisation by for beaches, the fit improves
considerably when the reef face slope is used instead of the beach
face (Fig. ). However, the runup parameterisations fail
to predict the runup during extreme wave conditions. This is mainly
attributed to the underestimation of wave setup. However it is worth
noting that the good fit of the R2% parameterisation is
ascribed to a combination of the over-prediction of S and under-prediction of setup. Therefore, future work should be devoted to
improving such parameterisations by incorporating the reef geometry
characteristics in the formulations.
Conclusions
A numerical model was employed for the theoretical study of the role
of the reef–dune system in coastal protection against extreme wave
events in Puerto Morelos (Mexico). The storm impact scale proposed by
shows that ecosystem degradation enhances beach
vulnerability, particularly for storms with return periods smaller
than 10 years. The combined degradation of both the dune and reef
further increases the vulnerability, so that the conservation of the
system as a whole is important for coastal protection. This implies
that the environmental service of coastal protection by coral reefs
and dunes is critical in the short term regarding infrastructure
losses in coastal areas. Neglecting the storm surge contribution
significantly underestimated the storm impact scale, particularly for
return periods of less than 3 years. For the reef setting studied
here, both the infragravity swash and the wave-induced setup play an
important role when parameterising runup. The inclusion of the reef
slope improves the model fit to numerical data, suggesting that the
equations used for beach environments need to incorporate reef
geometry characteristics. However, the main drawback in the present
study is that it does not consider the dune or the beach as erodible
features. Both play an important role in energy dissipation and hence
further research is warranted to investigate their effect on
increasing/decreasing the storm impact during extreme
events. Furthermore, the role of reef roughness and two-dimensional
horizontal processes needs to be addressed for a more comprehensive
study on the implication of reef degradation in such environments.
The numerical results and data employed in this work can be
obtained on request from the author.
GF carried out all the numerical simulations and data analysis and helped to design the numerical tests.
ATF led and supervised this work and designed the numerical experiments. GM developed the scripts for downscaling the wave
hindcast data and reconstructing the runup time series. MEAA compiled and helped implement the numerical models in the cluster.
CA generated the wave hindcast information employed in this work. GF prepared the manuscript with contribution from all
co-authors.
The authors declare that they have no conflict of
interest.
Acknowledgements
The first author is funded by a postdoctoral scholarship awarded by the
Programa de Becas Posdoctorales UNAM-DGAPA. Financial support for this study
was provided by the National Council of Science and Technology CONACyT
through the National Coastal Resilience Laboratory (LANRESC), CB-2016-01
(project 284430), and the Institute of Engineering UNAM. Alec
Torres-Freyermuth, Gabriela Medellín, and Ma. Eugenia Allende-Arandia
acknowledge support provided by Cátedras CONACYT project 1146. Many
thanks to Gonzalo Martín Ruiz and José López González for
technical support, to CINVESTAV-Mérida for providing the beach profile,
and to CONABIO for the bathymetry. Jeff Hansen and two anonymous reviewers helped to significantly improve the manuscript. Finally, we acknowledge Delft University of Technology for making the development of SWASH possible. Edited by: Oded
Katz Reviewed by: Jeff Hansen and two anonymous referees
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